US Secretary of State Rex Tillerson insists he's staying at Foggy Bottom despite reports that, after one humiliation on top of another from President Donald Trump, he threatened to quit.

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Despite Tillerson's ineptitude as secretary, his departure wouldn't be altogether welcome. He is part of the Trump administration's "sane caucus" led by Defence Secretary James Mattis, bringing rational judgment to decisions on explosive foreign-policy issues involving North Korea, Iran, Russia and the Persian Gulf. The counter caucus is led by Trump himself.

Perhaps Trump was wrong to tap a chief executive of ExxonMobil to manage US foreign policy; the history of CEOs moving to top cabinet posts is mixed at best. But Tillerson never had a fair chance. The latest conflict with his erratic boss came last weekend, while Tillerson was in China working on a diplomatic approach to North Korea's nuclear threat. Trump publicly blasted the effort, writing on Twitter: "I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man..."

Still, it's impossible to defend Tillerson's tenure. He has ignored or alienated much of the foreign service, and mid-career diplomats are leaving in droves. US foreign policy will pay a price for this brain drain well after Trump is gone.

Tillerson is politically tone-deaf. He doesn't appreciate the importance of public diplomacy, he has a weak staff and he hasn't cultivated good relations with Congress.

Two pillars of the Republican foreign-policy establishment, former defence secretary Bob Gates and former secretary of state James Baker, urged Tillerson to take the job, hoping that his international business experience would be helpful to a neophyte president. Another wise predecessor, George Shultz, counselled that the most important initial task was to forge a good relationship with Trump.

Tillerson tried, but his effort proved futile. Trump ignored his chief diplomat, allowing him to be undercut by his son-in-law, Jared Kushner. And that was before the public humiliation.

In August, Tillerson distanced himself from Trump's bigoted comments in sympathy with the far-right and neo-Nazi agitators who incited violence in Charlottesville, Virginia.

Mattis has been more successful. For one thing, he's better versed in the ways of Washington. He also appeals to Trump on a visceral level, though for the wrong reason; the president, who fancies himself a tough guy, loves that Mattis's Marine nickname was "Mad Dog." He may not know that it's an ill-chosen label that Mattis doesn't like.

Many Washington observers expect Tillerson to be replaced by UN Ambassador Nikki Haley. A former governor of South Carolina, Haley has displayed a good sense of public diplomacy, is politically skilful and excels at one key magic trick: She knows how to flatter Trump.